To determine which inequality Willow solved based on the number line representation, we see that there is an open circle at 4.5, which implies that 4.5 is not included in the solution set. The line extending to negative 10 indicates that the solution includes all values less than 4.5.
The appropriate inequality would be one that results in a solution set of \( x < 4.5 \).
Now, let's evaluate each response:
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\( x + 2\frac{1}{2} < 2\frac{1}{2} \)
- This is equivalent to \( x + 2.5 < 2.5 \), which simplifies to \( x < 0 \). (Not the answer)
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\( x - 2\frac{1}{3} < 2\frac{1}{6} \)
- This is equivalent to \( x - \frac{7}{3} < \frac{13}{6} \). Solving gives us: \[ x < \frac{13}{6} + \frac{7}{3} = \frac{13}{6} + \frac{14}{6} = \frac{27}{6} \] \[ x < 4.5 \] (This could work, but let's keep looking)
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\( x - 1.5 \leq 3 \)
- This simplifies to \( x \leq 4.5 \). We cannot have a closed interval with an open circle at 4.5. (Not the answer)
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\( x + 1.25 \leq 5.75 \)
- This simplifies to \( x \leq 4.5 \). Again, we cannot have a closed interval with an open circle at 4.5. (Not the answer)
The only option that provides the inequality \( x < 4.5 \) while also satisfying the open circle condition is the second option.
Therefore, the correct answer is: \( x - 2\frac{1}{3} < 2\frac{1}{6} \)